A Phenomenological analysis on isospin-violating decay of $X(3872)$

Abstract

In a molecular scenario, we investigate the isospin-breaking hidden charm decay processes of $X(3872)$, i.e., $X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$, $X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^{0}J/\psi$, and $X(3872)\to {\pi }^0{\chi }_{cJ}$. We assume that the source of the strong isospin violation comes from the different coupling strengths of $X(3872)$ to its charged components $D^{\ast +}{D}^{-}$ and neutral components $D^{\ast 0}{\bar{D}}^0$ as well as the interference between the charged meson loops and neutral meson loops. The former effect could fix our parameters by using the measurement of the ratio $\Gamma [X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^{0}J/\psi ]/\Gamma [X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi ]$. With the determined parameter range, we find that the estimated ratio $\Gamma [X(3872)\to {\pi }^0{\chi }_{c1}/\Gamma [X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi ]$ is well consistent with the experimental measurement from the BESIII collaboration. Moreover, the partial width ratio of ${\pi }^0{\chi }_{cJ}$ for $J=0,1,2$ is estimated to be $1.77\sim 1.65:1:1.09\sim 1.43$, which could be tested by further precise measurements of BESIII and Belle II.

11 pages, 7 figures, accepted for publication in the Eur.Phys.J.C

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• Observation of sizeable $\omega$ contribution to ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$ decays
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• Search for $X(3872)\to {\pi }^0{\chi }_{c0}$ and $X(3872)\to \pi \pi {\chi }_{c0}$ at BESIII
• Pole trajectories from $S$- and $P$-wave $D{\bar{D}}^{\ast }$ interactions
• Constrain the ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ effective couplings via the $X(3872)\to {\pi }^0{\chi }_{cJ}$ decays
• The $X(3872)\to J/\psi \pi \gamma$ and $X(3872)\to J/\psi \pi \pi \gamma$ decays
• Two-body strong decays of the hidden-charm tetraquark molecular states via the QCD sum rules
• Exotic hadrons associated with $b$-quark
• Insights into the nature of the $X(3872)$ through B meson decays